You are here

A Course in Number Theory and Cryptography

Edition:

2

Publisher:

Springer

Number of Pages:

225

Price:

64.95

ISBN:

978-0-387-94293-3

This book suffers from having too many goals: it attempts to be an introduction to both number theory and to cryptography, by studying the overlap between the two subjects, and it attempts to be an introduction to computational number theory. The portion of number theory that is used in cryptography is a minuscule part of all number theory, and reading this book will not give you a good idea of what number theory is about. Cryptography is a large, complex, and rapidly-growing subject, so studying the parts that deal with number theory teaches you only a tiny corner of cryptography. Computational number theory is not a subject most people would be interested in unless they already knew something about number theory, and although the book has reasonable coverage of this topic, it is not well-motivated for the intended reader.

Given these limitations, the book is well done. It is presented as applied number theory, and it does have good coverage of applications, including RSA encryption and primality testing. It has an algorithmic orientation, including estimates of computational costs of all the algorithms. There are lots of numerical examples, although only very simple ones, because the book was published in 1994 and assumes the reader won’t have access to computers. A Very Good Feature is that it includes solutions to all the exercises.

About one-third of the book is devoted to factorization methods, even though these don’t have much, if anything, to do with cryptography, and this is where most of the computational number theory is. The material here is good and still fairly up-to-date. A good book strictly on factorization is David Bressoud’s Factorization and Primality Testing, that covers roughly the same topics in these areas but in more depth.